{"id":236171,"date":"2025-06-16T05:38:15","date_gmt":"2025-06-16T05:38:15","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=236171"},"modified":"2025-06-16T05:38:17","modified_gmt":"2025-06-16T05:38:17","slug":"the-factorisation-of-x2-5x-6-yields","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/16\/the-factorisation-of-x2-5x-6-yields\/","title":{"rendered":"The factorisation of – x2 + 5x – 6 yields"},"content":{"rendered":"\n

The factorisation of – x2 + 5x – 6 yields (a) – (x – 2)(3 – x) (b) – (2 – x) (3 – x) (c) (x – 2)(x – 3) (d) (2 + x) (3 – x)<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct answer is: (b) – (2 – x)(3 – x)<\/strong><\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

Start by analyzing the given quadratic expression:\u2212x2+5x\u22126- x^2 + 5x – 6\u2212x2+5x\u22126<\/p>\n\n\n\n

To factor this expression, consider removing the negative sign for easier handling:\u2212(x2\u22125x+6)- (x^2 – 5x + 6)\u2212(x2\u22125x+6)<\/p>\n\n\n\n

Now focus on factoring the expression inside the parentheses:x2\u22125x+6x^2 – 5x + 6×2\u22125x+6<\/p>\n\n\n\n

This quadratic has a standard form ax2+bx+cax^2 + bx + cax2+bx+c, where:<\/p>\n\n\n\n

    \n
  • a=1a = 1a=1<\/li>\n\n\n\n
  • b=\u22125b = -5b=\u22125<\/li>\n\n\n\n
  • c=6c = 6c=6<\/li>\n<\/ul>\n\n\n\n

    Look for two numbers that multiply to 6 and add to -5. These numbers are:<\/p>\n\n\n\n

      \n
    • -2 and -3<\/li>\n<\/ul>\n\n\n\n

      Therefore, the expression factors as:x2\u22125x+6=(x\u22122)(x\u22123)x^2 – 5x + 6 = (x – 2)(x – 3)x2\u22125x+6=(x\u22122)(x\u22123)<\/p>\n\n\n\n

      So the original expression becomes:\u2212(x\u22122)(x\u22123)- (x – 2)(x – 3)\u2212(x\u22122)(x\u22123)<\/p>\n\n\n\n

      This form can be manipulated into different but equivalent forms. Applying the property of signs:\u2212(x\u22122)(x\u22123)=\u2212(2\u2212x)(3\u2212x)- (x – 2)(x – 3) = – (2 – x)(3 – x)\u2212(x\u22122)(x\u22123)=\u2212(2\u2212x)(3\u2212x)<\/p>\n\n\n\n

      This works because:x\u22122=\u2212(2\u2212x),x\u22123=\u2212(3\u2212x)x – 2 = – (2 – x), \\quad x – 3 = – (3 – x)x\u22122=\u2212(2\u2212x),x\u22123=\u2212(3\u2212x)<\/p>\n\n\n\n

      So:(x\u22122)(x\u22123)=[\u2212(2\u2212x)][\u2212(3\u2212x)]=(2\u2212x)(3\u2212x)(x – 2)(x – 3) = [ – (2 – x) ] [ – (3 – x) ] = (2 – x)(3 – x)(x\u22122)(x\u22123)=[\u2212(2\u2212x)][\u2212(3\u2212x)]=(2\u2212x)(3\u2212x)<\/p>\n\n\n\n

      However, due to the negative outside the brackets, it results in:\u2212(x\u22122)(x\u22123)=\u2212(2\u2212x)(3\u2212x)- (x – 2)(x – 3) = – (2 – x)(3 – x)\u2212(x\u22122)(x\u22123)=\u2212(2\u2212x)(3\u2212x)<\/p>\n\n\n\n

      Thus, the equivalent and correct factorization is:<\/p>\n\n\n\n

      – (2 – x)(3 – x)<\/strong><\/p>\n\n\n\n

      This matches option (b)<\/strong>.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      The factorisation of – x2 + 5x – 6 yields (a) – (x – 2)(3 – x) (b) – (2 – x) (3 – x) (c) (x – 2)(x – 3) (d) (2 + x) (3 – x) The Correct Answer and Explanation is: The correct answer is: (b) – (2 – x)(3 – x) […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-236171","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236171","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=236171"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236171\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=236171"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=236171"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=236171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}